题目：Adaptive FEM for Helmholtz equation with large wave number
报告人：武海军 教授（南京大学）
邀请人：沈晓芹 教授（hbs02红宝石线路数学系）
报告时间：2023年4月13日下午5:00-6:30
报告地点：hbs02红宝石线路会议室9-320
摘要: A posteriori upper and lower bounds are derived for the finite element method (FEM) for the Helmholtz equation with large wavenumber. It is proved rigorously that the standard residual type error estimator seriously underestimates the true error of the FE solution for the mesh size $h$ in the preasymptotic regime, which is first observed by [Babuska,~et~al., A posteriori error estimation for finite element solutions of Helmholtz equation. Part I, Int. J. Numer. Meth. Engrg. 40, 3443--3462 (1997)] for a one dimensional problem. By establishing an equivalence relationship between the error estimators for the FE solution and the corresponding elliptic projection of the exact solution, an adaptive algorithm is proposed and its convergence and quasi-optimality are proved under the condition that $k^{2p+1}h_0^{2p}$ is sufficiently small, where $k$ is the wavenumber, $h_0$ is the initial mesh size.
报告人简介：武海军，南京大学数学系教授、博导，国家杰出青年基金获得者，江苏省数学会秘书长。研究领域包括高波数散射问题有限元方法、界面问题的非拟合界面罚有限元方法等等。2012年获江苏省数学杰出成就奖，2015年获国家杰出青年科学基金资助。
